This will basically do it at the most simple level:
"use strict";
var name = "foo";
var func = new Function(
"return function " + name + "(){ alert('sweet!')}"
)();
//call it, to test it
func();
If you want to get more fancy, I have a written an article on "Dynamic function names in JavaScript".
~ Answered on 2012-03-30 17:39:30